QuestionMay 5, 2026

10. Simplify the expression. sqrt (125t^4r^3s^13)

10. Simplify the expression. sqrt (125t^4r^3s^13)
10. Simplify the expression. sqrt (125t^4r^3s^13)

Solution
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Answer

5t^2rs^6\sqrt{5rs} Explanation 1. Factor perfect squares 125 = 25 \cdot 5, so \sqrt{125} = \sqrt{25 \cdot 5} = 5\sqrt{5}. t^4 is a perfect square: \sqrt{t^4} = t^2. r^3 = r^2 \cdot r: \sqrt{r^2} = r, leftover \sqrt{r}. s^{13} = s^{12} \cdot s: \sqrt{s^{12}} = s^6, leftover \sqrt{s}. 2. Combine results Outside: 5 \cdot t^2 \cdot r \cdot s^6. Inside: \sqrt{5 \cdot r \cdot s}.

Explanation

1. Factor perfect squares <br /> $125 = 25 \cdot 5$, so $\sqrt{125} = \sqrt{25 \cdot 5} = 5\sqrt{5}$. <br />$t^4$ is a perfect square: $\sqrt{t^4} = t^2$. <br />$r^3 = r^2 \cdot r$: $\sqrt{r^2} = r$, leftover $\sqrt{r}$. <br />$s^{13} = s^{12} \cdot s$: $\sqrt{s^{12}} = s^6$, leftover $\sqrt{s}$. <br /><br />2. Combine results <br /> Outside: $5 \cdot t^2 \cdot r \cdot s^6$. Inside: $\sqrt{5 \cdot r \cdot s}$.
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